Front-end user interface

flux_balance_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
)

Compute an optimal objective-optimizing solution of the given model.

Most arguments are forwarded to optimized_values.

Returns a tree with the optimization solution of the same shape as given by flux_balance_constraints.

flux_balance_constraints(
    model::AbstractFBCModels.AbstractFBCModel;
    interface,
    interface_name
) -> Any

A constraint tree that models the content of the given instance of AbstractFBCModel.

The constructed tree contains subtrees fluxes (with the reaction-defining "variables") and flux_stoichiometry (with the metabolite-balance-defining constraints), and a single constraint objective thad describes the objective function of the model.

Optionally if interface is specified, an "interface block" will be created within the constraint tree for later use as a "module" in creating bigger models (such as communities) using interface_constraints. The possible parameter values include:

• nothing – default, no interface is created
• :sbo – the interface gets created from model's SBO annotations)
• :identifier_prefixes – the interface is guesstimated from commonly occurring adhoc reaction ID prefixes used in contemporary models
• :boundary – the interface is created from all reactions that either only consume or only produce metabolites

Output interface name can be set via interface_name.

See Configuration for fine-tuning the default interface creation.

flux_variability_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    objective_bound,
    reactions,
    optimizer,
    settings,
    workers
)

Perform a Flux Variability Analysis (FVA) on the model, and return a dictionary of flux ranges where the model is able to perform optimally.

The constraint system is constructed using flux_balance_constraints, and the variability is examined on all reaction's fluxes, or on the subset given optionally in reaction_subset (e.g., reaction_subset = ["PFK", "ACALD"]). The optimality tolerance can be specified with objective_bound using e.g. relative_tolerance_bound or absolute_tolerance_bound; the default is 99% relative tolerance.

Parameter workers may be used to enable parallel or distributed processing; the execution defaults to all available workers. Other parameters (esp. optimizer) are internally forwarded to optimized_values.

Use constraints_variability to customize the FVA execution.

linear_parsimonious_flux_balance_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    tolerances,
    kwargs...
)

Like parsimonious_flux_balance_analysis, but uses the L1-metric parsimonious system given by linear_parsimonious_flux_balance_constraints.

In turn, the solution is often faster, does not require a solver capable of quadratic objectives, and has many beneficial properties of the usual parsimonious solutions (such as the general lack of unnecessary loops). On the other hand, like with plain flux balance analysis there is no strong guarantee of uniqueness of the solution.

Solver configuration arguments are forwarded to parsimonious_optimized_values.

linear_parsimonious_flux_balance_constraints(
    model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
) -> ConstraintTrees.Tree{ConstraintTrees.Constraint}

Like parsimonious_flux_balance_constraints, but uses a L1 metric for solving the parsimonious problem. The parsimonious_objective constraint is thus linear.

parsimonious_flux_balance_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    tolerances,
    kwargs...
)

Compute a parsimonious flux solution for the model, using the constraints given by parsimonious_flux_balance_constraints.

In short, the objective value of the parsimonious solution should be the same as the one from flux_balance_analysis, except the squared sum of reaction fluxes is minimized. If there are multiple possible fluxes that achieve a given objective value, parsimonious flux thus represents the "minimum energy" one, which is arguably more realistic.

Solver configuration arguments are forwarded to parsimonious_optimized_values.

parsimonious_flux_balance_constraints(
    model::AbstractFBCModels.AbstractFBCModel
) -> Any

A constraint system like from flux_balance_constraints, but with the parsimonious objective present under key parsimonious_objective. Best used via parsimonious_flux_balance_analysis.

linear_metabolic_adjustment_minimization_analysis(
    model::AbstractFBCModels.AbstractFBCModel,
    args...;
    optimizer,
    settings,
    reference_parsimonious_optimizer,
    reference_parsimonious_settings,
    reference_optimizer,
    reference_settings,
    kwargs...
)

Perform a linear minimization of metabolic adjustment analysis (l-MOMA) on model. The reference is given by the second argument, which is either a reference_flux or a reference_model (the second argument is forwarded to linear_metabolic_adjustment_minimization_constraints).

While the solution is "less uniquely defined" than with fully quadratic metabolic_adjustment_minimization_analysis, the linear variant typically produces a sufficiently good result with much less resources. See documentation of linear_parsimonious_flux_balance_analysis for some of the considerations.

linear_metabolic_adjustment_minimization_constraints(
    model::AbstractFBCModels.AbstractFBCModel,
    reference_model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
) -> Union{Nothing, ConstraintTrees.Tree{ConstraintTrees.Constraint}}

Like metabolic_adjustment_minimization_constraints but the output constraints optimize the L1 distance from the linear-parsimonious solution of the reference_model.

linear_metabolic_adjustment_minimization_constraints(
    model::AbstractFBCModels.AbstractFBCModel,
    reference_fluxes::ConstraintTrees.Tree;
    _...
) -> ConstraintTrees.Tree{ConstraintTrees.Constraint}

Like metabolic_adjustment_minimization_constraints but optimizes the L1 distance from reference_fluxes.

Keyword arguments are discarded for compatibility with the other overload.

metabolic_adjustment_minimization_analysis(
    model::AbstractFBCModels.AbstractFBCModel,
    args...;
    optimizer,
    settings,
    reference_parsimonious_optimizer,
    reference_parsimonious_settings,
    reference_optimizer,
    reference_settings,
    kwargs...
)

Find a solution of the "minimization of metabolic adjustment" (MOMA) analysis for the model, which is the "closest" feasible solution to the solution given in the second argument, which is either reference_fluxes or reference_model (see documentation of metabolic_adjustment_minimization_constraints), in the sense of squared-sum distance. The minimized squared distance (the objective) is present in the result tree as minimal_adjustment_objective.

If the second argument is a reference model, it is solved using a parsimonious_flux_balance_analysis with the optimizer and settings parameters for the 2 steps set by keyword arguments prefixed by reference_.

This is often used for models with smaller feasible region than the reference models (typically handicapped by a knockout, a nutritional deficiency or a similar perturbation). MOMA solution then gives an expectable "easiest" adjustment of the organism towards a somewhat working state.

Reference fluxes that do not exist in the model are ignored (internally, the objective is constructed via squared_sum_error_value).

metabolic_adjustment_minimization_constraints(
    model::AbstractFBCModels.AbstractFBCModel,
    reference_model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
) -> Any

A slightly easier-to-use version of metabolic_adjustment_minimization_constraints that computes the reference flux as the parsimonious optimal solution of the reference_model. The reference flux is calculated using reference_optimizer and reference_modifications, which default to the optimizer and settings.

Other arguments are forwarded to the internal call of parsimonious_optimized_values.

Returns nothing if no feasible solution is found.

metabolic_adjustment_minimization_constraints(
    model::AbstractFBCModels.AbstractFBCModel,
    reference_fluxes::ConstraintTrees.Tree;
    _...
) -> Any

Keyword arguments are discarded for compatibility with the other overload.

log_concentration_constraints(
    model::AbstractFBCModels.AbstractFBCModel;
    reactions,
    metabolites,
    metabolite_concentration_bound,
    reaction_concentration_bound
) -> ConstraintTrees.Tree{ConstraintTrees.Constraint}

Build log-concentration-stoichiometry constraints for the model, as used e.g. by max_min_driving_force_analysis.

The output constraint tree contains a log-concentration variable for each metabolite from model, in subtree log_concentrations. The total reactant log-concentrations for each reaction are constrained in subtree log_concentration_stoichiometry. By default, all reactions and metabolites in model are included.

A concentration bound is given by parameter function concentration_bound for each metabolite ID (the string ID is the single argument of the function); by default the function returns nothing and no bounds are installed. The same is used for reactions with reaction_concentration_bound.

mutable struct Isozyme

A simple struct storing information about the isozyme composition, including subunit stoichiometry and turnover numbers. Use with enzyme_constrained_flux_balance_analysis.

Fields

• gene_product_stoichiometry::Dict{String, Float64}: Mapping of gene product identifiers ("genes" in FBC model nomenclature) to their relative amount required to construct one unit of the isozyme.

• kcat_forward::Union{Nothing, Float64}: Turnover number for this isozyme catalyzing the forward direction of the reaction.

• kcat_reverse::Union{Nothing, Float64}: Turnover number for this isozyme catalyzing the reverse direction of the reaction.

enzyme_constrained_flux_balance_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
)

Perform the enzyme-constrained flux balance analysis on the model and return the solved constraint system.

Arguments are forwarded to enzyme_constrained_flux_balance_constraints; solver configuration arguments are forwarded to optimized_values.

enzyme_constrained_flux_balance_constraints(
    model::AbstractFBCModels.AbstractFBCModel;
    reaction_isozymes,
    gene_product_molar_masses,
    capacity,
    interface,
    interface_name
)

Construct a enzyme-constrained flux-balance constraint system, following the method in GECKO algorithm (refer to: Sánchez, Benjamín J., et al. "Improving the phenotype predictions of a yeast genome‐scale metabolic model by incorporating enzymatic constraints." Molecular systems biology 13.8 (2017): 935).

The enzyme mass constraints depend primarily on the available isozymes, given in parameter reaction_isozymes, which is a mapping of reaction identifiers to descriptions of Isozymes that may catalyze the particular reactions. The isozymes are built from gene products, the mass of which is specified by gene_product_molar_masses. In total, the amount of gene product building material is limited by capacity.

capacity may be a single number, which sets the mass limit for "all described enzymes". Alternatively, capacity may be a vector of identifier-genes-limit triples that together form a constraint (identified by the given identifier) that limits the total sum of the listed genes to the given limit.

interface and interface_name are forwarded to flux_balance_constraints.

simplified_enzyme_constrained_flux_balance_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
)

Perform the enzyme-constrained flux balance analysis on the model and return the solved constraint system.

Arguments are forwarded to simplified_enzyme_constrained_flux_balance_constraints; solver configuration arguments are forwarded to optimized_values.

simplified_enzyme_constrained_flux_balance_constraints(
    model;
    reaction_isozymes,
    gene_product_molar_masses,
    capacity,
    interface,
    interface_name
)

Like enzyme_constrained_flux_balance_constraints, but automatically selects a single "fastest" isozyme for each reaction direction. In turn, the system requires much less variables in the constraint system description, and usually solves more efficiently, for the price of possibly finding suboptimal solutions. The method follows the SMOMENT algorithm described in Bekiaris, P.S., Klamt, S. Automatic construction of metabolic models with enzyme constraints. BMC Bioinformatics 21, 19 (2020). https://doi.org/10.1186/s12859-019-3329-9.

Arguments are as with enzyme_constrained_flux_balance_constraints, with a major difference in capacity handling: the identifier lists (2nd elements of the triples given in the list) are not identifiers of gene products, but identifiers of reactions.

community_flux_balance_analysis(args...; kwargs...)

Run the Community Flux Balance Analysis on several models. All arguments are forwarded to community_flux_balance_constraints which constructs the model; this function returns the solved model.

community_flux_balance_constraints(
    model_abundances,
    community_exchange_bounds;
    interface,
    interface_exchanges,
    interface_biomass,
    default_community_exchange_bound
) -> ConstraintTrees.Tree{ConstraintTrees.Constraint}

Construct an instance of a linear community Flux Balance Analysis (cFBA) model. The relative abundances of the organisms are known in advance; this function predicts the maximum achievable community growth rate.

model_abundances is a dictionary-like object that maps model identifiers to tuples of models (usually subtypes of AbstractFBCModel) and their abundances (such as: "bug1" => (bug1, 0.5), ...). community_exchange_bounds is a dictionary-like object that can be additionally used to restrict selected community exchange reactions (keys should be reaction IDs, the values are converted to ConstraintTrees-like bounds). Bounds otherwise default to parameter default_community_exchange_bound, which itself defaults to nothing (i.e., unbounded).

If required, constraint trees may be supplied instead of AbstracFBCModels in model_abundances. These must provide an interface compatible with interface_exchanges and interface_biomass.

interface is forwarded to flux_balance_constraints. interface_exchanges and interface_biomass are used to pick up the correct interface part to contribute to the community exchanges and community biomass.

objective_production_envelope(
    model::AbstractFBCModels.AbstractFBCModel,
    reactions::Vector{String};
    breaks,
    optimizer,
    settings,
    workers
)

Find the objective production envelope of the model in the dimensions given by reactions.

This runs a variability analysis of the fluxes given by flux_balance_constraints to determine an applicable range for the dimensions, then splits the dimensions to equal-sized breaks (of count breaks for each dimension, i.e. total breaks ^ length(reactions) individual "multidimensional breaks") thus forming a grid, and returns an array of fluxes through the model objective with the individual reactions fixed to flux as given by the grid.

optimizer and settings are used to construct the optimization models.

The computation is distributed to the specified workers, defaulting to all available workers.

gene_knockout_constraints(
    fluxes::ConstraintTrees.Tree{ConstraintTrees.Constraint},
    knockout_genes,
    model::AbstractFBCModels.AbstractFBCModel
) -> ConstraintTrees.Tree{ConstraintTrees.Constraint}

Make a ConstraintTree that simulates a gene knockout of knockout_genes in the model and disables corresponding fluxes accordingly.

Keys of the fluxes must correspond to the reaction identifiers in the model.

knockout_genes may be any collection that support element tests using in. Since the test is done many times, a Set is a preferred contained for longer lists of genes.

All constraints are equality constraints returned in a single flat ConstraintTree.

gene_knockout_constraints(
    fluxes::ConstraintTrees.Tree{ConstraintTrees.Constraint},
    knockout_gene::String,
    model::AbstractFBCModels.AbstractFBCModel
) -> ConstraintTrees.Tree{ConstraintTrees.Constraint}

Convenience overload of gene_knockout_constraints for knocking out a single gene (without the necessity to store the gene identifier in a singleton container).

gene_knockouts(
    model::AbstractFBCModels.AbstractFBCModel;
    ...
)
gene_knockouts(
    model::AbstractFBCModels.AbstractFBCModel,
    gene_combinations::Vector{<:Union{String, Tuple{Vararg{String, N}} where N}};
    kwargs...
)

Compute the objective value of the model for all knockouts specified by gene_combinations, which is a vector of gene IDs or tuples of gene IDs that are knocked out in groups.

Returns a vector in the same order as gene_combinations.

Extra arguments (mainly, the optimizer) are forwarded to screen_optimization_model.

loopless_flux_balance_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
)

Perform the loopless flux balance analysis on the model, returning the solved constraint system.

Arguments are forwarded to loopless_flux_balance_constraints (see the documentation for the description of the constraint system); solver configuration arguments are forwarded to optimized_values.

loopless_flux_balance_constraints(
    model::AbstractFBCModels.AbstractFBCModel;
    flux_infinity_bound,
    driving_force_nonzero_bound,
    driving_force_infinity_bound
) -> ConstraintTrees.Tree{ConstraintTrees.Constraint}

Construct a flux-balance constraint system from model with added quasi-thermodynamic constraints that ensure that thermodynamically infeasible internal cycles can not occur. The method is closer described by: Schellenberger, Lewis, and, Palsson. "Elimination of thermodynamically infeasible loops in steady-state metabolic models.", Biophysical journal, 2011`.

The loopless condition comes with a performance overhead: the computation needs to find the null space of the stoichiometry matrix (essentially inverting it); and the subsequently created optimization problem contains binary variables for each internal reaction, thus requiring a MILP solver and a potentially exponential solving time.

Internally, the system is constructed by combining flux_balance_constraints and loopless_constraints.

The arguments driving_force_max_bound and driving_force_nonzero_bound set the bounds (possibly negated ones) on the virtual "driving forces" (G_i in the paper).

max_min_driving_force_analysis(
    model::AbstractFBCModels.AbstractFBCModel;
    kwargs...
)

Perform the max-min driving force analysis on the model, returning the solved constraint system.

Arguments are forwarded to max_min_driving_force_constraints (see the documentation for the description of the constraint system); solver configuration arguments are forwarded to optimized_values.

max_min_driving_force_constraints(
    model::AbstractFBCModels.AbstractFBCModel;
    reaction_standard_gibbs_free_energies,
    reference_flux,
    concentration_ratios,
    constant_concentrations,
    ignored_metabolites,
    proton_metabolites,
    water_metabolites,
    concentration_lower_bound,
    concentration_upper_bound,
    T,
    R,
    reference_flux_atol
)

Create max-min driving force constraint system from model, using the supplied reaction standard Gibbs free energies in reaction_standard_gibbs_free_energies.

The method is described by: Noor, et al., "Pathway thermodynamics highlights kinetic obstacles in central metabolism.", PLoS computational biology, 2014.

reference_flux sets the directions of each reaction in model. The scale of the values is not important, only the direction is examined (w.r.t. reference_flux_atol tolerance). Ideally, the supplied reference_flux should be completely free of internal cycles, which enables the thermodynamic consistency. To get the cycle-free flux, you can use loopless_flux_balance_analysis (computationally demanding, but gives thermodynamically consistent solutions), parsimonious_flux_balance_analysis or linear_parsimonious_flux_balance_analysis (which is computationally simple, but the consistency is not guaranteed).

Internally, log_concentration_constraints is used to lay out the base structure of the problem.

Following arguments are set optionally:

• water_metabolites, proton_metabolites and ignored_metabolites allow to completely ignore constraints on a part of the metabolite set, which is explicitly recommended especially for water and protons (since the analyses generally assume aqueous environment of constant pH)
• constant_concentrations can be used to fix the concentrations of the metabolites
• concentration_lower_bound and concentration_upper_bound set the default concentration bounds for all other metabolites
• concentration ratios is a dictionary that assigns a tuple of metabolite-metabolite-concentration ratio constraint names; e.g. ATP/ADP ratio can be fixed to five-times-more-ATP by setting concentration_ratios = Dict("adenosin_ratio" => ("atp", "adp", 5.0))
• T and R default to the usual required thermodynamic constraints in the expected units (the defaults assume the "usual" units, valuing 298.15 K and ~0.008314 kJ/K/mol, respectively). These multiply the log-concentrations to obtain the actual Gibbs energies, and thus driving forces.

flux_sample(
    model::AbstractFBCModels.AbstractFBCModel;
    seed,
    objective_bound,
    method,
    n_chains,
    collect_iterations,
    optimizer,
    settings,
    workers,
    kwargs...
)

Run a sampling algorithm on the near-optimal feasible space of the model (as specified by objective_bound). By default, the sampling algorithm is ACHR (the method parameter is defaulted to sample_chain_achr). The sampling algorithm is ran for n_chains and the iterations for collecting the sampled values are specified by collect_iterations.

optimizer is used to generate the warmup (with settings) for the sampler using the usual unidimensional maximum-variability fluxes (as from flux_variability_analysis). All computations are parallelized across workers.

Extra arguments are forwarded to sample_constraints. Eventually the arguments will reach the method function, so extra arguments can be also used to customize the methods (e.g., by setting the epsilon for the ACHR sampler).